Generally, both can be heat-seeking, dumb-fire, guided or whatever.
The big difference tends to be in size, speed and payload.
Missiles movereallyreallyfastandblowyourwingofflikeaboltoflightning... whereas torpedoes tend to move much slower, but blow almost anything to kingdom come.
Torps tend to be what you use to kill a big Capship and various space sims often have missions where you, as a small fighter, have to chase down and destroy incoming torp salvos before they hit your carrier/mothership.
Torps are also usually very big, so a single-pilot combat vessel tends to carry only a few of them rather than full racks (think of the missiles you see on an AH-64 Apache) of them.